Chajda, Ivan; Länger, Helmut Groupoids assigned to relational systems. (English) Zbl 1274.08002 Math. Bohem. 138, No. 1, 15-23 (2013). Summary: By a relational system we mean a couple \((A,R)\) where \(A\) is a set and \(R\) is a binary relation on \(A\), i.e., \(R\subseteq A\times A\). To every directed relational system \(\mathcal {A}=(A,R)\) we assign a groupoid \({\mathcal G}({\mathcal A})=(A,\cdot )\) on the same base set where \(xy=y\) if and only if \((x,y)\in R\). We characterize basic properties of \(R\) by means of identities satisfied by \({\mathcal G}({\mathcal A})\) and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems. Cited in 3 Documents MSC: 08A02 Relational systems, laws of composition 20N02 Sets with a single binary operation (groupoids) Keywords:relational system; groupoid; directed system; \(g\)-homomorphism PDFBibTeX XMLCite \textit{I. Chajda} and \textit{H. Länger}, Math. Bohem. 138, No. 1, 15--23 (2013; Zbl 1274.08002) Full Text: Link